Jump in to Part 2 of my chat with Peter Liljedahl! In this episode Peter and I dug into the concepts that will likely come up in your consolidating.
Did you miss Part 1? Listen in here where Peter Liljedahl and I chat about consolidation in a Thinking Classroom.
On This Episode with Peter Liljedahl
- How students represent their thinking
- How representations can move students from simple understanding to more sophisticated understanding
- How having multiple ways to represent and understand a math concept is what peter calls a Thick Understanding
- How you Build a Thinking Classroom when you have a pacing guide and standards you must teach
- Productive struggle
When I say that this episode is JAM packed with goodness… I mean it.
About Peter Liljedahl
💻 Peter’s website: https://www.peterliljedahl.com/
🛜 Facebook Group – Building Thinking Classrooms
📝 Building a Thinking Classroom in Math (Article on Edutopia by Peter)
5 Representations of Thinking
*From NCTM, Principles to Actions: Ensuring Mathematical Success for All
- Talking it (verbal)
- Symbolically representing (Numbers)
- Drawings of tools (Physical or Visual)
2 Schools of Thoughts About Representations
- Multiple representations thickens their understanding
- Multiple representations mediate from A to B
Multiple Representations Thicken Understanding
When we can think about different representations of square numbers it creates a thick understanding, so in the future when I see a square number I have multiple representations to tap into. SO I have multiple ways of thinking about a task. It gives me more receptors when a task is posed. I have more representations that I can access to understand a task.
Tax Collector
A popular task from Building Thinking Classrooms – find it in Chapter 6
Thin Understanding → Describes students that are adding from left to right and ignoring place value. They have a thin understanding of addition
Multiple Representations Move Us from A to B
Physical Manipulatives → Drawing → Symbolic → Abstract Understanding
Using representations can be mediators
Example: Using a ruler (number line) to subtract in younger years, but in 9th grade we want students to have an abstract/symbolic understanding of subtraction
Best way to ensure students have a Thick Understanding & are moving from Physical to Virtual to Abstract is to always require them to have at least 2 representations in their work.
- talking & writing
- tools & talking
- drawing & talking
So… be sure your students are:
Describing the model they drew.
Talking about the context and writing a number sentence to match.
Using manipulatives and discussing how they relate to the context
“Thick Understanding allows you to be more flexible and more strategic in being more effective or efficient in their problem solving.” -Mona
You can’t actually force people to learn things in your timeframe
Somedays the discussion things just kinda fizzle out and you don’t get to that nice clear learning target but we will try again tomorrow. This is a HUGE mindset shift.
We can…
- bring the student to the water, but we can’t make them drink
All we can do is till the soil and hope that something grows.
So… we have to be nimble.
If they aren’t making the connections then we can ask ourselves “What can I do?”
- I can give them a hint.
- Show a representations
- Send them to observe another group
- Be patient
- Give what I can
- Evaluate ask, “where are we today?”
Consolidation in Any Form
“Move from Bottom Up”
Start with something everyone can do and understand. Common, easiest, concrete way of thinking about this task and then move up. That way we are moving through every child’s zone of proximal development & were able to lift everyone a little bit.
At the end of a consolidation everyone should be a little further along than they were at the beginning. But they shouldn’t ALL be up at the ceiling– that’s too big of a lift. We have to be responsive to what we have in the room that day. You may have had the best laid plans (Your threshold), but we have to be willing to raise or lower the threshold based on what your students are doing and understanding.
This is harder to do than you think.
Peter Liljedahl’s Take on Pacing Guides & Learning Goals
{John SanGiovanni and I dug into this topic on our interview– Listen here}
Peter Liljedahl acknowledges the reality of pacing guides and standards, but urges teachers to 👉🏾 Ask yourself, “Achieve some learning or achieve no learning”
In pursuit of the intended learning goal, sometimes only just a few kids will learn and others will learn nothing.Alternatively, we could have had all kids move a little closer toward the goal, and maybe not all achieve the goal… but everyone could learn a bit instead of only a couple kids mastering the learning target.
✨Nudge students along in their learning journey.✨
It doesn’t mean that every child is going to master every standard on that day.
The better you know your standards or content and understand it more and do this more you can better help them along on their journey.
Peter Liljedahl discussed how a teacher asked him during a lesson observation, “What are you paying attention to?”
He reflects on this by saying: “We have been trained to pay attention to the errors and the math because we’re pursuing the right answer. Instead, we have to focus on the learner, body language.
Attend to Students’ Body Language
Body language can tell the teacher everything they need to know.
As you’re monitoring solving… Read the room’s body language.
Body language can tell you where students are in their learning. Their emotions are telling me about their progress.
However, Peter Liljedahl acknowledges how difficult this can be by saying…
“When we teach math the students get in the way.”
“When we teach students the math get in the way.”
We have to be aware of the balance between teaching the student & math
Productive Struggle
Check out this episode all about productive struggle & the research that supports it!
Reflecting on what you’re paying attention to when there’s productive struggle.
Teachers Ask:
“What do you do when they’re getting it all wrong during productive struggle?”
– Pay attention to the student & if they’re showing you with their body language that they’re still productive let them keep going
Productive Struggle in a Thinking Classroom:
- Challenge doesn’t equal productive struggle
- Meet challenge on the heels of success they are more willing to productively struggle
- Quick wins = success and then they are willing to be challenged
Confidence & self efficacy is build through those quick wins and allow students to struggle
What Do We Do Tomorrow?
- Do self reflection. Where are you right now? You might not be ready for consolidation. Establish routines for yourself & your students first.
- Do I have a convergent or divergent task?
- Divergent- capture different ways of thinking for a gallery walk. In 5 minutes, look at three boards. Keep it simple!
- Convergent- have a sequence of tasks that get harder. Floor- middle- ceiling & ask students to put the tasks in order. Let them stand & you scribe.
**don’t over think it
Lightbulb moments happen during consolidation. “Never Skip the Debrief”… but realize you won’t always hit a home run!
Be sure to stop along YOUR journey to reflect and acknowledge the successes you are experience in your classroom and celebrate that! Reflect on the opportunities you’re giving your students to think in math is such a gift.
Other Related Episodes:
Interview with Peg Smith, Author of 5 Practices Listen Here
3 Common Mistakes when Trying Something New in Math Class Listen Here
Mentioned in this Episode
📘 Building Thinking Classrooms
📕 Modify your Building Thinking Classroom
🔥 MY TEACHER HOT TAKE 🔥
- Teacher PD should match the TEACHER’S goals, not the schools goals.
- PD should be provided by teachers, that understand what it’s like to teach in this post-covid world.
That’s why I’m providing low cost PD series for you. (ONLY $11!!) 🤩
Each PD is designed with actionable strategies that I used in my own classroom and I know work with students who struggle.
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Have Questions? 📱 My DMs on IG are always open@hellomonamath